Aalborg Universitet
Power flow analysis for droop controlled LV hybrid AC-DC microgrids with virtual
impedance
Li, Chendan; Chaudhary, Sanjay K.; Quintero, Juan Carlos Vasquez; Guerrero, Josep M.
Published in:
Proceedings of the IEEE Power & Energy Society General Meeting, PES 2014
DOI (link to publication from Publisher):
10.1109/PESGM.2014.6939887
Publication date:
2014
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Li, C., Chaudhary, S., Vasquez, J. C., & Guerrero, J. M. (2014). Power flow analysis for droop controlled LV
hybrid AC-DC microgrids with virtual impedance. In Proceedings of the IEEE Power & Energy Society General
Meeting, PES 2014. (pp. 1-4). IEEE Press. DOI: 10.1109/PESGM.2014.6939887
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Power flow analysis for droop controlled LV hybrid
AC-DC microgrids with virtual impedance
Chendan Li, Sanjay K. Chaudhary, Juan C. Vasquez, and Josep M. Guerrero
Department of Energy Technology, Aalborg University
Aalborg, Denmark
{che , skc , juq , joz}@et.aau.dk
Abstract— The AC-DC hybrid microgrid is an effective form of
utilizing different energy resources and the analysis of this
system requires a proper power flow algorithm. This paper
proposes a suitable power flow algorithm for LV hybrid AC-DC
microgrid based on droop control and virtual impedance. Droop
and virtual impedance concepts for AC network, DC network
and interlinking converter are reviewed so as to model it in the
power flow analysis. The validation of the algorithm is verified
by comparing it with steady state results from detailed time
domain simulation. The effectiveness of the proposed algorithm
makes it a potential method for planning, dispatching and
operation of droop controlled LV hybrid AC-DC.
Index Terms—hybrid AC-DC microgrid, droop control, virtual
impedance, power flow.
I.
INTRODUCTION
Recent technology development and practice in power
system has witnessed increasing interests on the concept of
“direct DC”, from the adoption of High-voltage direct-current
(HVDC) transmission systems when connecting offshore
wind farms or large distance interconnected grids, to energy
efficient applications in distribution system that utilize DC
power directly from the source residentially or commercially
for the purpose of avoiding DC-AC-DC power conversions.
Among these applications, DC microgrid, which comprises
distributed generation, energy storage systems and local
loads as a local grid, is gaining more interests due to its
potential to integrate increasing DC renewable source and
load, such as , electrical vehicles, photovoltaic systems, fuel
cells, or LEDs , with high efficiency. The application of DC
microgrids have increasingly been found its way in data
centers, telecom system, and some buildings and offices.
DC microgrids are, however, not likely to fully replace
an existing AC microgrid due to the long historical
development of the AC power system. The architecture of the
coexistence of AC and DC subgrids intertied by an
electronically controlled power converter is here to stay [1][5]. The structure of an example of hybrid AC-DC microgrid
is shown in Fig. 1. This hybrid network consists of two DC
subgrids and one AC subgrid, and the main grid is connected
with it by an intelligent bypass switch.
One of the main purposes of the management for the
microgrid is the control of the power flow. To achieve this
goal, among many control strategies, hierarchical control
DC microgrid
EV charging
PV
DC microgrid
DC Load
IBS
PCC
Interlinking
converter
Main
Utility Grid
WT
AC Load Batteries
EV charging
Flywheel
AC microgrid
Figure 1.
Structure of an example of hybrid AC-DC microgrid
methodology is proposed in [1] as a generalized and even
standard way for AC microgrid and DC microgrid. The steady
state power distribution is the direct control outcome of the
primary control of the hierarchical control.
To make the planning, dispatch and operation more
economical and reliable, a steady state power flow analysis for
a microgrid is always desired. For this purpose, a lot of work
has been done [6]−[8], but they all aimed at the AC microgrid
only. Moreover, to a certain extent, none of them is suitable
for Low voltage AC microgrid, either because they use
conventional concepts of PQ, PV and slack buses in the
modelling or due to that they overlooked the effect of the
virtual impedance[7]. Power flow analysis for AC-DC power
system is not a new topic, yet many of them are addressed for
HVDC system thus not suitable for a hybrid microgrid with its
unique power flow control based on droop and virtual
impedance[9]-[11].
This paper, a power flow for hybrid AC-DC microgrid is
proposed considering the droop control with virtual
impedance and power flow among microgrids through
interlinking converter control. The paper is organized as
follows. In the second section, power flow control strategy
based on the droop control and virtual impedance for single
microgrid and intertied microgrids are reviewed as
background knowledge to justify the choice of modelling
method in the next section. In the third section, mathematical
model of proposed power flow analysis is presented based on
the control discussed previously. The verification of the
proposed algorithm by comparing the results from calculation
and the steady state results from time domain simulation is
provided in the fourth section which shows the effectiveness
of the algorithm. Finally, section five gives the conclusions
and the future work.
II.
DROOP CONTROL AND VIRTUAL IMPEDANCE SCHEME IN
Where VGi(DC) is the voltage reference to DC source which
should be equal to the measured voltage value in a stable
DC source using virtual impedance control
VG (DC)
V 0(DC)
MICROGRIDS
A. For a single LV AC microgrid
The concept of the droop control with virtual impedance is
illustrated in Fig.2. As is shown in it, when the virtual
impedance Zv equals zero, i.e., virtual impedance is not used,
the output characteristic of generation is controlled by the
droop equation as (1) and (2) to mimic the synchronous
generator in the bulk grid.
-
VG
Virtual impedance
Iline
Rline
RD
DC Bus i
DC Bus i+1
Figure 3. Concept of droop control using virtual impedance in a single
DC microgrid
load which is usually modified from secondary control to
achieve voltage regulation, RDi is the virtual impedance of the
Line impedance
+
Z v  Rv  j Lv
Virtual Droop Bus
+
system in the steady state, V0i (DC) is the output reference at no
AC source generation using virtual impedance
control
Vdroop
-
Iline
Line resistance
Virtual resistance
droop controller, and iGi (DC) is the output current of the DC
Z line
AC Bus i
AC Bus i+1
Figure 2. Concept of droop control with virtual impedance in a single
AC microgrid
f *  f 0i  K Pi PGi
(1)
| VGi || VG 0i |  KQiQGi
(2)
Being f0i, KPi, PGi,VG0i, KQi, QGi the nominal frequency,
proportional frequency droop parameter, real power
generation, nominal voltage, proportional voltage amplitude
droop parameter, and reactive power at generator i,
respectively.
But when the virtual impedance is added in the control so
as to decouple real and reactive power when the line
impedance is not inductive enough, it changes the output
voltage characteristics of the generation as is shown in (3).
VG  Vdroop  I G Z v
 Vdroop  (YGbusVG ) Z v
(3)
Where the Vdroop is the voltage matrix of the virtual droop
bus, I Gline the injection current matrix in the generation bus,
YGbus the admittance matrix of the network directed connected
to the generation buses, Z v the virtual impedance matrix of
the controller and VG the voltage matrix of generation bus
(assume all the generation buses are droop controlled).
B. For a single LV DC microgrid
The principle of the droop control for LV DC microgrid is
illustrated in Fig. 3. In fact, the realization of droop control in
DC microgrid is through the use of the virtual resistance RD.
DC sources in a network cannot work as stiff voltage sources
for there will be circulating current. The droop concept has
thus come into being by multiplication of measured voltage
deviation to a value reciprocal to the virtual resistance. The
concept is illustrated by (4).
VGi (DC)  V0i (DC)  RDi iGi (DC)
(4)
source.
C. For intertied microgrids
Droop concepts can also be applied to two different
microgrids by controlling the interlinking converter as are
proposed in [1]-[4]. Although the droop concept is used in the
control of the interlinking converter, the interlinking converter
cannot be seen as a droop controlled converter to each
interconnected side as in a single microgrid. There are mainly
two control objectives which are realized by using droop
concepts. One is aiming at making the two intertied connected
microgrids being studied share all the load equally [2], another
is aiming at making the two intertied microgrids equally
stressed and minimize the interlinking energy flow by
controlling the power transferred according to the load
condition of the two microgrids [3]. Despite different control
objectives, to make the droop coefficients comparable, the
variables used for sharing the real power as the signals need to
be normalized to common per unit range. Moreover, despite
different control strategy the ultimate given to the interlinking
converter is the transferred power through it. To make the
model of the interlink converter control strategy independent,
the generalized form of the power flow control in the
interlinking converter can be show in fig. 4. The direction of
the arrow indicates the positive direction of the power.
Reactive power cannot be transferred through the interlinking
converter and that is why there is only Qc1 in the AC side. The
transferred real power satisfies the following equations
consider the converter power loss and the possible energy
storage system in the DC link of the converter.
AC
microgrid
PC1
DC
microgrid
PC 2
Interlinking
converters
QC1
AC Bus i
DC Bus k
Figure 4. Concept of droop control with virtual impedance in a single
AC microgrid
Pc 2  Pc1  Ploss  Pstorage
(5)
f 0i  f 0 g  KPi PGi  K Pg PGg  0
MATHEMATICAL MODEL OF POWER FLOW IN LV
HYBRID AC-DC MICROGRID
f 0i  KPi PGi  f 0 g  KPg PGg
(6)
(16)
(17)
n
Pi  Vi V j (Gij cosij  Bij sin ij )
(7)
Qi  Vi V j (Gij cosij  Bij sin ij )
(8)
Where θij，Gij and Bij are the bus admittance angle, the
conductance and the susceptance, respectively.
For DC buses, it is possible to assume the network is pure
resistive in its steady state model. According to the Kirchhoff's
current law, that current injected at the bus i equals to the
current flowing to other buses, the network equation can be
written as follows:
n
(9)
j 1
j i
Where I i (DC) is the DC injection current in bus i, Yij (DC) is
the admittance between the bus i and bus j, and Vi (DC) is the
voltage magnitude in bus i;
Pdc ,i
 Ydc ,ij (Vdc ,i  Vdc , j )
Vdc ,i
j 1
(18)
j i
VGi (DC)  V0i (DC)  RD
PGi (DC)
(19)
VGi (DC)
PGi (DC)  PDi (DC)  Pdc,i  Pc 2  0
IV.
(20)
ALGORITHM VERIFICATION ON A TEST HYBRID
MICROGRID
The validity of the algorithm is verified using a 10-bus
hybrid microgrid by comparing the results from calculation
and the steady state results from time domain simulation with
the toolbox SimPowerSystems of Matlab as is shown in Fig.5.
According to [3], it defines four basic rules for the control of
transferred power, the real power flow will have three
different cases: scenario 1, real power flows from AC side to
DC side; scenario 2, real power flows form DC side to AC
side; and scenario 3, no power flows in between. Since the last
case is equivalent to calculate two separated AC network and
DC network, only first two cases are tested. The network data
and control parameters are listed in Table I.
n
 Yij (DC) (Vi (DC)  V j (DC) )
(10)
j 1
j i
AC Bus 1 AC Bus 4
Interlinking
Converter 1
DC Bus 1
DC source 1
AC source 1
Additionally, for the Droop-buses, there is one more
constraint they have to follow:
VGi (DC)  V0i (DC)  RDiiGi (DC)
(11)
AC Bus 2
AC Load 1
AC Bus 5
DC Load 1
AC Load 2
AC source 2
AC Bus 3 AC Bus 6
Where iGi (DC) can be written as,
DC Bus 2
Vi (DC)
(15)
VG  Vdroop  (YGbusVG )Z v  0
The network equations that all buses should obey are
given by:
Pi (DC)
(14)
PGi  PDi  Pi  Pc1  0
QGi  QDi  Qi  Qc1  0
where i=1,…, g-1, being g the number of the buses.
I i (DC)  Yij (DC) (Vi (DC)  V j (DC) )
(13)
| VG 0i |  | VGi |  KQiQGi  0
For the AC buses, taking into account that the frequency is
a global variable for all the DG buses throughout the
microgrid, from (1) we can obtain:
DC Bus 4
III.
DC Load 2
AC Load 3
DC source 2
Interlinking
Converter 2
AC source 3
DC Bus 3
iGi (DC) 
PGi (DC)
VGi (DC)
Figure 5. Single line diagram of test hybrid micogrid
(12)
Considering the virtual impedance constraint (3) for AC
buses, and assuming there is no energy storage in the DC link
and the power loss in the converter is not significant which is
reasonable in LV small microgrid system, the overall
mathematical model of power flow analysis for a hybrid
microgrid is as follows:
TABLE I.
THE NETWORK DATA AND CONTROL PARAMETERS OF TEST
HYBRID MICROGRID
paramaters
symbol
value
units
frequency droop for DG1
KP1
0.001
rad/(W · s)
amplitude droop for DG1
KQ1
0.02
V/Var
frequency droop for DG2
KP2
0.0005
rad/(W · s)
amplitude droop for DG2
KQ2
0.01
V/Var
frequency droop for DG3
KP3
0.004
rad/(W · s)
amplitude droop for DG3
KQ3
0.002
V/Var
DC bus 1
0.99035
1100.73
0.99986
1094.29
Virtual resistor
Rv_i(i=1,2,3)
0.1
Ω
DC bus 3
0.98693
594.441
0.99981
593.08
Virtual inductor
Lv_i(i=1,2,3)
0.004
H
AC bus 1
0.98891
1023.02
0.99009
1023.03
reference voltage in DC
bus 1
reference voltage in DC
bus 2
Virtual resistance for DC
source 1
Virtual resistance for DC
source 2
bus number
Vref1
48
V
AC bus 2
0.99090
2046.04
0.99211
2046.07
Vref2
48
V
AC bus 3
0.98839
511.513
0.98957
511.52
Rd1
0.2
Ω
Rd2
0.5
Ω
Rload(Ω)
Lload(mH)
DC bus 2
5
0
DC bus 4
3
0
AC bus 4
100
0
AC bus 5
100
0
AC bus 6
100
0.25136H
from bus
to bus
Line
resistance(Ω)
DC bus 1
DC bus 2
0.05
line
inductance
(mH)
0
DC bus 2
DC bus 3
0.04
0
DC bus 3
DC bus 4
0.08
0
DC bus 4
DC bus 1
0.03
0
AC bus 1
AC bus 4
0.15
0. 062
AC bus 2
AC bus 5
0.21
0.096
AC bus 3
AC bus 6
0.11
0.048
AC bus 4
AC bus 5
0.12
0.031
AC bus 5
AC bus 6
0.15
0.062
V.
In scenario 1, real power 200W and 300W is flowing from
AC network to DC network through interlinking converter 1
and 2 respectively. The comparison results of generation buses
are shown in Table II.
TABLE II.
COMPARISON RESULTS WHEN REAL POWER FROM AC TO DC
SimPowerSystem results
Power Flow Results
Node
Mag.(p.u.)
Power(W)
Mag.(p.u.)
Power(W)
DC bus 1
0.99541
525.76
0.99993
520.79
DC bus 3
0.99597
184.812
0.99994
182.4
AC bus 1
0.97680
1289.07
0.97661
1287.94
AC bus 2
0.97947
2578.13
0.97921
2575.87
AC bus 3
0.97562
644.532
0.97547
643.97
In scenario 2, the real power 200W and 300W is flowing
from DC network to AC network. The comparison results of
generation buses are shown in Table III.
TABLE III.
COMPARISON RESULTS WHEN REAL POWER FROM DC TO AC
SimPowerSystem results
Power Flow Results
Node
Mag.(p.u.)
Power(W)
Mag.(p.u.)
From these two sets of power flow results comparisons for
the generation buses, it shows that the calculated values are
close to the simulation thus verifies the effectiveness of the
proposed algorithm.
Power(W)
CONCLUSION
A power flow algorithm suitable for droop controlled LV
hybrid AC-DC microgrid has been proposed where the virtual
impedance is used in both the AC network, DC network and
the interlinking converter. The validation of the proposed
power flow algorithm is verified by comparing the results
from time domain simulation and that from calculation
through this algrothm. Coincidence of the results shows that
this power flow algorithm can be used as a tool to analyze the
steady state response of the hybrid microgrid which uses
droop and virtual impedance as its control strategy.
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